873edo: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Infobox ET}}
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
{{ED intro}}
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-07-14 17:10:55 UTC</tt>.<br>
 
: The original revision id was <tt>241393981</tt>.<br>
873edo is [[consistent]] to the [[7-odd-limit]], but the error of [[harmonic]] [[3/1|3]] is quite large. The equal temperament is most notable for [[tempering out]] the [[amity comma]], 1600000/1594323, in the 5-limit, providing the [[optimal patent val]] for it.
: The revision comment was: <tt></tt><br>
 
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
=== Odd harmonics ===
<h4>Original Wikitext content:</h4>
{{Harmonics in equal|873}}
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">The //873 equal division// divides the octave into 873 equal parts of 1.375 cents each. It tempers out the amity comma, 1600000/1594323, in the 5-limit, providing the [[optimal patent val]]. </pre></div>
 
<h4>Original HTML content:</h4>
=== Subsets and supersets ===
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;873edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;873 equal division&lt;/em&gt; divides the octave into 873 equal parts of 1.375 cents each. It tempers out the amity comma, 1600000/1594323, in the 5-limit, providing the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt;.&lt;/body&gt;&lt;/html&gt;</pre></div>
Since 873 factors into {{factorization|873}}, 873edo has subset edos {{EDOs| 3, 9, 97, and 291 }}.  
 
[[Category:Amity]]

Latest revision as of 16:30, 20 February 2025

← 872edo 873edo 874edo →
Prime factorization 32 × 97
Step size 1.37457 ¢ 
Fifth 511\873 (702.405 ¢)
Semitones (A1:m2) 85:64 (116.8 ¢ : 87.97 ¢)
Consistency limit 7
Distinct consistency limit 7

873 equal divisions of the octave (abbreviated 873edo or 873ed2), also called 873-tone equal temperament (873tet) or 873 equal temperament (873et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 873 equal parts of about 1.37 ¢ each. Each step represents a frequency ratio of 21/873, or the 873rd root of 2.

873edo is consistent to the 7-odd-limit, but the error of harmonic 3 is quite large. The equal temperament is most notable for tempering out the amity comma, 1600000/1594323, in the 5-limit, providing the optimal patent val for it.

Odd harmonics

Approximation of odd harmonics in 873edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +0.450 -0.059 +0.246 -0.474 -0.115 -0.665 +0.391 -0.488 -0.606 -0.678 -0.096
Relative (%) +32.8 -4.3 +17.9 -34.5 -8.4 -48.4 +28.5 -35.5 -44.1 -49.3 -7.0
Steps
(reduced) 		1384
(511) 		2027
(281) 		2451
(705) 		2767
(148) 		3020
(401) 		3230
(611) 		3411
(792) 		3568
(76) 		3708
(216) 		3834
(342) 		3949
(457)

Subsets and supersets

Since 873 factors into 32 × 97, 873edo has subset edos 3, 9, 97, and 291.

Retrieved from "https://en.xen.wiki/index.php?title=873edo&oldid=181885"